1. ## Re: Help please simplifying this equation to be graphed

You have never told us completely and exactly what the problem is. Nor have you given us any clue about your level of mathematical knowledge. Consequently, it is very difficult to give you an answer that is both relevant and understandable by you.

You graph functions, not equations. Now it is very remotely possible that the mess you are given defines IMPLICITLY a single function in one independent and one dependent variable, but in all probability it defines implicitly a number of different functions with one independent variable. Determing what function or functions can be restated as explicit functions in two variables may be theoretically conceivable, but it looks dauntingly ugly even if possible.

However, you can also think about the expression on the left as being an explicit function with two independent variables and one dependent variable. I greatly doubt that there is any practical way to graph that three dimensional object in a comprehensible way.

Finally, you can think about this as an equation and forget all about graphing. It is easy to find solutions to the equation. What may be difficult is finding all the solutions.

$\{f(x,\ y)\}^2 + \{g(y)\}^2 = 0 \implies f\{(x,\ y)\}^2 = -\ \{g(y)\}^2.$

Now if x and y are supposed to be real numbers f(x, y) and g(y) are real numbers, which means that g(y) = 0. That lets you solve for y.

Do you understand what I am saying?

2. ## Re: Help please simplifying this equation to be graphed

Originally Posted by Kiefer77
so would that now simplify to...

= 2(y^2-6y+8)i
It is impossible for the simplification to contain i.

All terms in the original have been squared: anything squared ends up non-negative.

This is the original:
Let k = |x-2| + |x-4] - 2 ; then original =
[(y - x/2 - 1)^2 + k]^2 * [(y - 3)^2 +k]^2
That cannot end up negative...

3. ## Re: Help please simplifying this equation to be graphed

Originally Posted by JeffM
If y is real, then $4((y^2 - 6y + 8)^2$ is non-negative.
My head is spinning: Jeff, isn't that positive, regardless of y's value?
The darn thing is squared...so result can't be negative.
What d'hell am I missing?

4. ## Re: Help please simplifying this equation to be graphed

Denis

$a = f(x,\ y)\ and\ b = g(x)\ and\ a^2 + b^2 = 0.$

If x and y are real, then a^2 and b^2 are necessarily both non-negative, but not necessarily positive. Two non-negatives that add to zero are necessarily both equal to zero.

Thus, y = 4 or y = 2. Now it is very easy to find quite a few x values that solve the equation. But to find all the potential x values is more work than I want to do on what seems to me to be a rather boring puzzle. Of course we have not even really been told what the puzzle is.

5. ## Re: Help please simplifying this equation to be graphed

It is a math puzzle. One that needs to be graphed to find the answer. One person I'm running against has already solved this puzzle by graphing this equation. My math skills are at the algebra level. If you are able to graph this equation, then you have a relevant answer for me. Also, if you're able to simplify this equation or are able to put in in slope form (y=mx+b) then that is also relevant. Or if you have another way to graph this equation, again, relevant.

I thought I needed to isolate or solve for y to make this into a slope formula thus making it easy to graph.

I think I'll try to simplify then plot graph. Meaning get rid of and combine as much as I can then just substitute say x = 0 and solve for y then y = 0 and solve for x.

6. ## Re: Help please simplifying this equation to be graphed

Jeff, you don't have to find all the x values. I've only asked for help simplifying the problem so I can plot graph using the simplified equation. Once this equation is graphed the image is my answer. I'm sorry if I haven't explained this clearly enough.

I noticed that no one has encouraged me to combine the absolute values or take the square root of both sides of the equation to knock out the ^2 on almost everything. I thought those were good ways to simply the equation. Was I wrong?

7. ## Re: Help please simplifying this equation to be graphed

You keep saying that it needs to be graphed to find the "answer." What is the exact problem statement?

8. ## Re: Help please simplifying this equation to be graphed

The reason that no one is encouraging you to take square roots is that it involves complex numbers. Furthermore, the square root of the long product is going to be some polynomial of very high degree in two variables.

9. ## Re: Help please simplifying this equation to be graphed

Any combination of y = 2 or 4 and x = 5, 8, 11, 19, 44, 47, 52, or 61 are solutions to the equation. There may be others, but that gives you 16 valid solutions. If you manage to simplify the implicit function defined by this equation, it will not be linear so
y = mx + b is not going to help.

10. ## Re: Help please simplifying this equation to be graphed

I've posted the exact problem twice. I can not find the words to explain this better. This equation has been graphed by one person already. After he graphed this equation the image was the answer to the puzzle. Let's say when he graphed this equation he drew an image of square, then the answer would be something like "square", "cube", or "box". Once the game is over I will find out how he did it and post his result here. Thank you for your efforts.
And by no means is this puzzle "boring" if we're all having this much difficulty solving it.

11. ## Re: Help please simplifying this equation to be graphed

You gave an equation, and normally what one does with an equation is to solve it. I have given you sixteen solutions so I am not having difficulty finding solutions to the equation. The jpg you posted twice did not say what the problem told you to do with that equation other than to solve it.

12. ## Re: Help please simplifying this equation to be graphed

My initial question, "Help please simplifying this equation to be graphed".

I see your 16 solutions but unfortunately I don't see how they will help me graph this equation. I'm looking for... "If x = a number, then y = this other number". But the equation in its current state is too damn long! LoL

At least I understand why y=mx+b won't work since the image won't be linear.

13. ## Re: Help please simplifying this equation to be graphed

&^(^%#\$@..Just noticed that the EQUATION is at the bottom of your attachment!
Why in hell did you not say so.
I'm outtahere...he's all yours, Jeffroi !!

14. ## Re: Help please simplifying this equation to be graphed

I'm with Denis. The real task is as likely to be see how many nerds you can get to waste their time on this.

15. ## Re: Help please simplifying this equation to be graphed

DenisB the equation is 23 lines long. I've shown this website to two other people on their own computers and they had no issue reading all 23 line of this math puzzle. Thank you for looking though. I've cursed at this problem for the last two weeks!

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